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8221 . a+b, $a^{2} - b^{2}$ এবং $a^{3} + b^{3}$ এর গ. সা.গু কত?

A. $a^{2} - b^{2}$
B. $a - b$
C. ${(a + b)}^{2}$
D. $a + b$

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Answer: Option D

Explanation:

১ম রাশি= a + b ২য় রাশি= a^{2} - b^{2} = (a + b) (a - b) {৩য় রাশি=a}^{3 +} {+b}^{3} = (a + b) (a^{2} - a b + b^{2}) ∴ নির্ণেয় গ.সা.গু= (a + b)

8222 . $9 a^{3} b^{2} c^{2}, 9 a^{3} b^{2} c^{2} 12 a^{2} b c, 15 a b^{3} c^{3}$ এর গ.সা.গু কোনটি?

A. 9abc
B. $9 a^{3} b^{3} c^{3}$
C. $3 a^{3} b^{3} c^{3}$
D. 3abc

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Answer: Option D

Explanation:

পোস্টাল অপারেটর ২৩.০৮.২০১৯

A. -22.5
B. -17.5
C. -10.5
D. 16

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Answer: Option B

Explanation:

যেহতু 1.5 সমীকরণটির একটি মূল সেহেতু ( 1.5)^2 + 1.5m + 24 = 0 2.25 + 1.5m + 24 = 0 m = - 26.25/1.5 m = - 17.5

8224 . $4 (x + y), 10 (x - y), 12 (x^{2} - y^{2})$ এর গ.সাগু কত?

A. x-y
B. x+y
C. 2
D. $12 (x^{2} - y^{2})$

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Answer: Option C

Explanation:

১ম রাশি=4 (a + b) =2×2 (a + b) ২য় রাশি=10 (a - b) =2×5 (a - b) ৩য় রাশি=12 (a^{2} - b^{2}) =2×3×2 (a + b) (a - b) ∴ নির্ণেয় গ.সা.গু=2

8225 . a2-3a,a3-9a এবং $a^{3} - 4 a^{2} + 3 a$ এর গ.সা.গু=?

A. a(a-3)
B. a-3
C. a
D. a(a+3)

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Answer: Option B

Explanation:

a² - 3a = a ( a - 3) a² - 9 = a² - 3² = (a+3) (a-3) a² - 4a + 3 = a² - 3a - a + 3 = a (a-3) - 1 (a-3) = (a-3) (a-1) নির্ণেয় গ.সা.গু = (a-3)

8226 . যদি $a^{3} - b^{3} = 513$ এবং $a - b = 3$ হয়, তবে ab এর মান কত?

A. 54
B. 35
C. 45
D. 55

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Answer: Option A

Explanation:

a^{3} - b^{3} = 513 \Rightarrow {(a - b)}^{3} + 3 a b (a - b) = 513 \Rightarrow {(3)}^{3} + 3 \times a b \times 3 = 513 \Rightarrow 27 + 9 a b = 513 \Rightarrow 9 a b = 513 - 27 \Rightarrow a b = \frac{486}{9} = 54

সমাজসেবা অধিদপ্তর নিয়োগ পরীক্ষা-২০১৮ | ফিল্ড সুপারভাইজার | ১৪.০৯.২০১৮

8227 . If $x + y = 7$ and $x^{2} + y^{2} = 25,$ then which one of the following equals the value of $x^{3} + y^{3} ?$

A. 7
B. 25
C. 65
D. 91

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Answer: Option D

Explanation:

দেওয়া আছে, x + y = 7 x^{2} + y^{2} = 25 \Rightarrow {(x + y)}^{2} - 2 x y = 25 \Rightarrow 7^{2} - 25 = 2 x y \Rightarrow 2 x y = 49 - 25 \Rightarrow x y = \frac{24}{2} = 12 x^{3} + y^{3} = {(x + y)}^{3} - 3 x y (x + y) = 7^{3} - 3 \times 12 \times 7 = 343 - 252 = 91

8228 . If x +y = 1/a and x-y =a then the value of $x^{2} - y^{2}$ is:

A. 4
C. 1
D. $a^{2}$

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Answer: Option C

Explanation:

দেওয়া আছে, x + y = \frac{1}{a} এবং x-y=a {এখন, x}^{2} {-y}^{2} = (x + y) (x - y) = \frac{1}{a} ×a=1

8229 . If a+b =8 and ab =15, what is the value of $a^{2} + b^{2} ?$

A. 94
B. 79
C. 34
D. 30

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Answer: Option C

Explanation:

আমরা জানি, {(a + b)}^{2} = a^{2} + 2 a b + b^{2} \Rightarrow {(8)}^{2} = a^{2} + b^{2} + 2 a b \Rightarrow 64 = a^{2} + b^{2} + (2 \times 15) \Rightarrow a^{2} + b^{2} + (2 \times 15) = 64 \Rightarrow a^{2} + b^{2} = 64 - 30 = 34

8230 . $x^{2} - 3 x, x^{2} - 9$ এবং $x^{2} - 4 x + 3$ বীজগাণিতীক রাশির গ. সা.গু কত হবে?

A. x-4
B. x + 3
C. x -3
D. x -1

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Answer: Option C

Explanation:

a² - 3a = a ( a - 3) a² - 9 = a² - 3² = (a+3) (a-3) a² - 4a + 3 = a² - 3a - a + 3 = a (a-3) - 1 (a-3) = (a-3) (a-1) নির্ণেয় গ.সা.গু = (a-3)

8231 . $x^{2} - y^{2}, x^{3} - y^{3}, x^{4} + x^{2} y^{2} + y^{4}$ রাশিগুলোর গ. সা.গু কত?

A. x+y
B. x -y
D. 1

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Answer: Option D

Explanation:

{১ম রাশি= x}^{2} {-y}^{2} = (x + y) (x - y) {২য় রাশি= x}^{3} {-y}^{3} = (x - y) (x^{2} + x y + y^{2}) {৩য় রাশি= x}^{4} {+x}^{2} y^{2} {+y}^{4} = {(x^{2})}^{2} {+2x}^{2} y^{2} + {(y^{2})}^{2} {-x}^{2} y^{2} = {(x^{2} + y^{2})}^{2} - {(xy)}^{2} = (x^{2} + y^{2} + x y) (x^{2} + y^{2} - x y) 1 ব্যাতীত কোনো সধারন উৎপাদক নেই। অতএব গ.সা.গু=1

8232 . What is the value of a If $3 x^{2} + a x + a + 3$ divisible $x + 2$

A. 12
B. 13
C. 14
D. 15

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Answer: Option D

Explanation:

8233 . $x + y = 5, x + 4 y = 4,$ what is the value of $4 x^{2} + 16 y^{2} ?$

A. 60
B. 40
C. 20
D. 80

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Answer: Option D

Explanation:

8234 . $x = a^{2} - 7 a + 6, y = a^{2} - 2 a + 1, z = a^{2} - 5 a + 4$ হলে x, y, z এর গ.সা.গু. কত?

A. $(a - 4)$
B. $(a - 1)$
C. $(a - 6)$
D. ${(a - 1)}^{2}$

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Answer: Option B

Explanation:

8235 . If $(x^{5} - 32) = 0$ and $x^{7} = 128,$ then,

A. X<0
B. X=2
C. X>3
D. X=5

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Answer: Option B

Explanation:

8223 . If one of the roots of the quadratic equation x^2+mx+24= 0 is x=1.5, then what is the value of m ?

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